Simulation results

To compare the performance of the proposed methods, we performed some simulations on an hybrid task set, composed of soft and hard tasks, using the scheduling simulator described in [3].

The task set is composed of 5 periodic hard tasks (fixed period, fixed execution time), which generate a hard load $U_{Hard}=\sum_{i = 1}^5 \frac{C_i}{T_i}=0.35$, and 3 soft tasks, whose interarrival and execution times are uniformly distributed around the mean values $\overline{t_{Soft}}$ and $\overline{c_{Soft}}$, being $U_{Soft}=3\frac{\overline{c_{Soft}}}{\overline{t_{Soft}}}$.

The performance of the algorithms has been evaluated measuring the mean Tardiness: the tardiness of a job is defined as 0 if the job finishes before $\overline{t_{Soft}}$, and the difference between the finishing time and $\overline{t_{Soft}}$ divided by $\overline{t_{Soft}}$ otherwise.

In the first experiment (Figure 3), we compare SFQ and EEVDF (using a quantum size of 1) against CBS. Using CBS, each hard task is scheduled by EDF, while soft tasks are scheduled by a dedicated server with parameters $(\overline{c_{Soft}},\overline{t_{Soft}})$; using a PS scheduler the weights are assigned so that no hard deadlines are missed, whereas all soft tasks have the same weight.

  

Figure 3: Mean tardiness experimented by CB and PS schedulers

Looking at Figure 3 it is easy to see that EEVDF and SFQ perform slightly better than CBS (because they are more fair), but this is due to the fact that we are using a very small quantum size.

  

Figure 4: Mean tardiness experimented by CB and PS schedulers

Although small quantum permits to reduce the mean tardiness, this causes a big number of context changes. To see this, Figure 5 shows the mean number of context switches experimented by a single task instance as a function of the quantum size, when a PS scheduler is used. Even using a quite small quantum (for example 10), the number of context switches enforced by the PS scheduler is much greater than the CBS (between 5 and 6 times). On the other hand, if the quantum size is increased to limit the number of context switches, the performance of a PS scheduler becomes closer to the CBS one.

  

Figure 5: Mean number of context switch per job

To show this, we performed a new experiment, in which EEVDF is used with a quantum size of 20. The results are shown in Figure 4. Further increasing the scheduling quantum size causes a waste of CPU bandwidth, so it is impossible to guarantee hard tasks using a proportional share scheduler with a too big quantum size.

  

Figure 6: Mean tardiness experimented by CB and PS schedulers

The performance of CBS can be increased (reducing the mean tardiness) using different parameters in order to emulate a PS scheduler (Q_s = Q, $T_s = \frac{Q_s}{B_s}$). Figure 6 shows the results of a forth experiment, in which each soft task is scheduled by a server with parameters Q_s=20 and $T_s = 20 \frac{\overline{t_{soft}}}{\overline{c_{soft}}}$, and the EEVDF quantum size is 20. As expected, the two results are similar.